https://file.aiquickdraw.com/mathbot/file/1726240632314p0kxqwfb.jpg

We are given a triangle where the perimeter is \(11x + 7\), and two sides of the triangle are labeled as \(5x + 5\) and \(3x - 1\). We need to find the missing side length, which I will call \(y\).

The formula for the perimeter of a triangle is the sum of all three sides. Therefore:

\[
\text{Perimeter} = \text{Side}_1 + \text{Side}_2 + \text{Side}_3
\]

Substitute the known values:

\[
11x + 7 = (5x + 5) + (3x - 1) + y
\]

Now, let's solve for \(y\).

First, simplify the equation:

\[
11x + 7 = 5x + 5 + 3x - 1 + y
\]

Combine like terms on the right-hand side:

\[
11x + 7 = 8x + 4 + y
\]

Now, isolate \(y\):

\[
y = 11x + 7 - 8x - 4
\]

Simplify further:

\[
y = 3x + 3
\]

So, the missing side length is \(y = 3x + 3\).

Would you like further details or have any additional questions?

Here are five related questions to consider:
1. What happens to the side lengths when specific values of \(x\) are substituted?
2. How would the solution change if the perimeter were altered?
3. Can this triangle be classified as a specific type (like equilateral or isosceles) based on the side lengths?
4. How would you calculate the area of this triangle given specific side lengths?
5. What is the relationship between the perimeter and area of a triangle?

**Tip:** Always double-check if an expression simplifies easily, as it can speed up problem-solving.

Find the missing side length of the following shape if the perimeter is 11x + 7.

Learn how to find the missing side length of a triangle using algebraic expressions. Given the perimeter of 11x + 7 and two side lengths of 5x + 5 and 3x - 1, we solve for the third side. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation